The phrase "adequacy of the linear" is grammatically correct and can be used in written English.
It can be used in contexts discussing the sufficiency or appropriateness of linear models or linear relationships in various fields such as mathematics, statistics, or engineering.
Example: "The adequacy of the linear model was assessed through residual analysis to ensure it fit the data appropriately."
Alternatives: "sufficiency of the linear" or "suitability of the linear".
Adequacy of the linear condition is explained from the viewpoints of stability margin and empirically-supported desirable closed-loop transfer functions.
The adequacy of the linear driving force rate expression as a simplified representation of the dynamic behaviour is investigated and it is shown that the simplified model provides an excellent approximation for a long column but breaks down when the column contains less than about twenty theoretical plates.
The adequacy of the linear regression equation was investigated using the R-square coefficient, which indicates how well data points fit a statistical model.
Linear adjustments were performed to have comparable measurements across laboratories; technical support for the adequacy of these linear adjustments was provided by microbiologists.
The adequacy of the developed linear models is examined through an analysis of variance (ANOVA).
We confirmed the adequacy of a linear term to model age, distance from major roadway, and cumulative traffic using penalized spline regression in the R software package (Free Software Foundation, Boston, MA).
In the Results section, we show that the data in Li et al. [12] provide experimental evidence that falsifies the adequacy of the type I and linear behaviors, yet corroborates the adequacy of type II behavior, (We purposely avoid the word "validate", taking the Popperian [34] view that scientific theories may only be falsified by experiments).
The corresponding initial linear section is shown as a thin dashed straight line which, in support of the adequacy of the fit, agrees quite well with the linear fit through the data for exposure at a mass of 5 μg.
The adequacy of the proposed model at 99% confidence level was confirmed by its high adjusted linear coefficient of determination (RAdj2= 0.9452).
The adequacy of the mathematical models established and the significance of the regression coefficients (i.e. linear, quadratic and interaction effects of the parameters) were analyzed using the analysis of variance (ANOVA).
